MULTIVALUED STOCHASTIC DELAY DIFFERENTIAL EQUATIONS AND RELATED STOCHASTIC CONTROL PROBLEMS

作     者：Diomande, Bakarime Maticiuc, Lucian 

作者机构：Alexandru Ioan Cuza Univ Fac Math Carol 1 Blvd 11 Iasi 700506 Romania Gheorghe Asachi Tech Univ Dept Math Carol 1 Blvd 11 Iasi 700506 Romania 

出 版 物：《QUAESTIONES MATHEMATICAE》 (数学问题)

年 卷 期：2017年第40卷第6期

页      面：769-802页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：project IDEAS [241/05.10.2011] 

主　　题：Multivalued SDE with delay dynamic programming principle Hamilton-Jacobi-Bellman equation viscosity solutions 

摘      要：We study the existence and uniqueness of a solution for the multivalued stochastic differential equation with delay (the multivalued term is of subdifferential type): {dX(t) + partial derivative phi(X(t)) dt is an element of b(t, X(t), Y(t), Z(t)) dt + sigma(t, X(t), Y(t), Z(t)) dW(t), t is an element of(s, T), X(t) = xi(t - s), t is an element of[s - delta, s]. Specify that in this case the coecients at time t depends also on previous values of X(t) through Y (t) and Z(t). Also X is constrained with the help of a bounded variation feedback law K to stay in the convex set Dom(phi). After wards we consider optimal problems where the state X is a soluction of a controlled delay stochastic system as above. We establish the dynamic programming principle for the value function and finally we prove that the value function is a viscosity solution for a suitable Hamilton-Jacobi-Bellman type equation.